/[escript]/trunk/paso/src/Solver_AMG.c
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Annotation of /trunk/paso/src/Solver_AMG.c

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Revision 2625 - (hide annotations)
Fri Aug 21 06:30:25 2009 UTC (10 years, 6 months ago) by jfenwick
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File size: 16611 byte(s)
Merging changes from new doco branch.
All docstrings are now in reStructured text.
A few email addresses have been fixes as well.
1 jfenwick 1851
2     /*******************************************************
3     *
4 jfenwick 2548 * Copyright (c) 2003-2009 by University of Queensland
5 jfenwick 1851 * Earth Systems Science Computational Center (ESSCC)
6     * http://www.uq.edu.au/esscc
7     *
8     * Primary Business: Queensland, Australia
9     * Licensed under the Open Software License version 3.0
10     * http://www.opensource.org/licenses/osl-3.0.php
11     *
12     *******************************************************/
13    
14    
15     /**************************************************************/
16    
17 artak 2475 /* Paso: AMG preconditioner */
18 jfenwick 1851
19     /**************************************************************/
20    
21 jfenwick 2625 /* Author: artak@uq.edu.au */
22 jfenwick 1851
23     /**************************************************************/
24    
25     #include "Paso.h"
26     #include "Solver.h"
27 artak 2475 #include "Options.h"
28 jfenwick 1851 #include "PasoUtil.h"
29 artak 1931 #include "UMFPACK.h"
30 artak 2507 #include "MKL.h"
31     #include "SystemMatrix.h"
32 phornby 1917 #include "Pattern_coupling.h"
33 jfenwick 1851
34     /**************************************************************/
35    
36     /* free all memory used by AMG */
37    
38     void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
39     if (in!=NULL) {
40     Paso_Solver_AMG_free(in->AMG_of_Schur);
41 artak 2112 Paso_Solver_Jacobi_free(in->GS);
42 jfenwick 1851 MEMFREE(in->inv_A_FF);
43     MEMFREE(in->A_FF_pivot);
44     Paso_SparseMatrix_free(in->A_FC);
45     Paso_SparseMatrix_free(in->A_CF);
46 artak 2556 Paso_SparseMatrix_free(in->A);
47 jfenwick 1851 MEMFREE(in->rows_in_F);
48     MEMFREE(in->rows_in_C);
49     MEMFREE(in->mask_F);
50     MEMFREE(in->mask_C);
51     MEMFREE(in->x_F);
52     MEMFREE(in->b_F);
53     MEMFREE(in->x_C);
54     MEMFREE(in->b_C);
55 gross 2551 #ifdef MKL
56     #else
57     #ifdef UMFPACK
58     Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
59     #endif
60     #endif
61     in->solver=NULL;
62     MEMFREE(in->b_C);
63 jfenwick 1851 MEMFREE(in);
64     }
65     }
66    
67     /**************************************************************/
68    
69     /* constructs the block-block factorization of
70    
71     [ A_FF A_FC ]
72     A_p=
73     [ A_CF A_FF ]
74    
75     to
76    
77     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
78     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
79    
80    
81     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
82    
83     then AMG is applied to S again until S becomes empty
84    
85     */
86 artak 2520 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
87 jfenwick 1851 Paso_Solver_AMG* out=NULL;
88 artak 2556 Paso_Pattern* temp1=NULL;
89     Paso_Pattern* temp2=NULL;
90 artak 2520 bool_t verbose=options->verbose;
91 jfenwick 1851 dim_t n=A_p->numRows;
92     dim_t n_block=A_p->row_block_size;
93     index_t* mis_marker=NULL;
94 artak 1881 index_t* counter=NULL;
95     index_t iPtr,*index, *where_p, iPtr_s;
96 artak 2107 dim_t i,k,j;
97 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
98 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
99 artak 2381 double S=0;
100 artak 2556 char fname[6];
101 artak 2475
102 artak 2439 /*Make sure we have block sizes 1*/
103 gross 2550 if (A_p->col_block_size>1) {
104     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
105     return NULL;
106     }
107     if (A_p->row_block_size>1) {
108     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
109     return NULL;
110     }
111 gross 2551 out=MEMALLOC(1,Paso_Solver_AMG);
112 jfenwick 1851 /* identify independend set of rows/columns */
113     mis_marker=TMPMEMALLOC(n,index_t);
114     counter=TMPMEMALLOC(n,index_t);
115 gross 2551 if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
116     out->AMG_of_Schur=NULL;
117     out->inv_A_FF=NULL;
118     out->A_FF_pivot=NULL;
119     out->A_FC=NULL;
120     out->A_CF=NULL;
121     out->rows_in_F=NULL;
122     out->rows_in_C=NULL;
123     out->mask_F=NULL;
124     out->mask_C=NULL;
125     out->x_F=NULL;
126     out->b_F=NULL;
127     out->x_C=NULL;
128     out->b_C=NULL;
129     out->GS=NULL;
130     out->A=Paso_SparseMatrix_getReference(A_p);
131     out->GS=NULL;
132     out->solver=NULL;
133     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
134     out->level=level;
135 artak 2556
136     sprintf(fname,"A%d.mat",level);
137 artak 2524
138 artak 2556 Paso_SparseMatrix_saveMM(A_p,fname);
139    
140 gross 2551 if (level==0 || n<=options->min_coarse_matrix_size) {
141     out->coarsest_level=TRUE;
142     #ifdef MKL
143     #else
144     #ifdef UMFPACK
145     #else
146     out->GS=Paso_Solver_getJacobi(A_p);
147     #endif
148     #endif
149     } else {
150     out->coarsest_level=FALSE;
151     out->GS=Paso_Solver_getJacobi(A_p);
152 artak 2442
153 gross 2551 /* identify independend set of rows/columns */
154     #pragma omp parallel for private(i) schedule(static)
155     for (i=0;i<n;++i) mis_marker[i]=-1;
156    
157     if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
158     Paso_Pattern_coup(A_p,mis_marker,options->coarsening_threshold);
159     }
160     else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
161     Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
162     }
163     else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
164     Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
165     }
166     else {
167     /*Default coarseneing*/
168 artak 2556 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
169 gross 2551
170 artak 2556 /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
171 gross 2551 }
172 artak 2475
173 gross 2551 if (Paso_noError()) {
174     #pragma omp parallel for private(i) schedule(static)
175     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
176 artak 2509
177 gross 2551 out->n=n;
178     out->n_block=n_block;
179     out->n_F=Paso_Util_cumsum(n,counter);
180     out->mask_F=MEMALLOC(n,index_t);
181     out->rows_in_F=MEMALLOC(out->n_F,index_t);
182     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
183     out->A_FF_pivot=NULL; /* later use for block size>3 */
184     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
185 jfenwick 1851 /* creates an index for F from mask */
186 artak 2107 #pragma omp parallel for private(i) schedule(static)
187 jfenwick 1851 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
188 artak 2107 #pragma omp parallel for private(i) schedule(static)
189 jfenwick 1851 for (i = 0; i < n; ++i) {
190     if (mis_marker[i]) {
191     out->rows_in_F[counter[i]]=i;
192     out->mask_F[i]=counter[i];
193     } else {
194     out->mask_F[i]=-1;
195     }
196     }
197 artak 2107
198     /* Compute row-sum for getting rs(A_FF)^-1*/
199 artak 2131 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
200 artak 1881 for (i = 0; i < out->n_F; ++i) {
201 artak 2107 S=0;
202 artak 2556 /*printf("%d : %d -> ",i, out->rows_in_F[i]);*/
203 artak 1881 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
204 artak 1975 j=A_p->pattern->index[iPtr];
205 artak 2556 /*if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);*/
206     if (mis_marker[j] && j==out->rows_in_F[i])
207     S=A_p->val[iPtr];
208 artak 1881 }
209 artak 2556 /*printf("-> %e\n",S);*/
210 artak 2442 out->inv_A_FF[i]=1./S;
211 artak 1881 }
212 gross 2551 }
213     }
214 jfenwick 1851
215 gross 2551 if ( Paso_noError()) {
216 jfenwick 1851 /* if there are no nodes in the coarse level there is no more work to do */
217     out->n_C=n-out->n_F;
218 gross 2551
219     /*if (out->n_F>500) */
220     out->rows_in_C=MEMALLOC(out->n_C,index_t);
221     out->mask_C=MEMALLOC(n,index_t);
222     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
223     /* creates an index for C from mask */
224     #pragma omp parallel for private(i) schedule(static)
225     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
226     Paso_Util_cumsum(n,counter);
227     #pragma omp parallel for private(i) schedule(static)
228     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
229     #pragma omp parallel for private(i) schedule(static)
230     for (i = 0; i < n; ++i) {
231     if (! mis_marker[i]) {
232 jfenwick 1851 out->rows_in_C[counter[i]]=i;
233     out->mask_C[i]=counter[i];
234     } else {
235     out->mask_C[i]=-1;
236     }
237 gross 2551 }
238     }
239     }
240     if ( Paso_noError()) {
241     /* get A_CF block: */
242     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
243     /* get A_FC block: */
244     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
245     /* get A_CC block: */
246     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
247    
248     }
249     if ( Paso_noError()) {
250     /*find the pattern of the schur complement with fill in*/
251 artak 2556 temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
252     temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
253     schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
254     Paso_Pattern_free(temp1);
255     Paso_Pattern_free(temp2);
256 gross 2551 }
257     if ( Paso_noError()) {
258     /* copy values over*/
259     #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
260     for (i = 0; i < schur_withFillIn->numRows; ++i) {
261     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
262     j=schur_withFillIn->pattern->index[iPtr];
263     iPtr_s=schur->pattern->ptr[i];
264     schur_withFillIn->val[iPtr]=0.;
265     index=&(schur->pattern->index[iPtr_s]);
266     where_p=(index_t*)bsearch(&j,
267 artak 2107 index,
268     schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
269     sizeof(index_t),
270     Paso_comparIndex);
271 gross 2551 if (where_p!=NULL) {
272     schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
273     }
274     }
275     }
276     Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
277     out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
278     }
279     /* allocate work arrays for AMG application */
280     if (Paso_noError()) {
281     out->x_F=MEMALLOC(n_block*out->n_F,double);
282     out->b_F=MEMALLOC(n_block*out->n_F,double);
283     out->x_C=MEMALLOC(n_block*out->n_C,double);
284     out->b_C=MEMALLOC(n_block*out->n_C,double);
285 artak 1890
286 gross 2551 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
287     #pragma omp parallel for private(i,k) schedule(static)
288     for (i = 0; i < out->n_F; ++i) {
289     for (k=0; k<n_block;++k) {
290     out->x_F[i*n_block+k]=0.;
291     out->b_F[i*n_block+k]=0.;
292 jfenwick 1851 }
293 gross 2551 }
294     #pragma omp parallel for private(i,k) schedule(static)
295     for (i = 0; i < out->n_C; ++i) {
296     for (k=0; k<n_block;++k) {
297     out->x_C[i*n_block+k]=0.;
298     out->b_C[i*n_block+k]=0.;
299     }
300     }
301     }
302 jfenwick 1851 }
303     }
304     }
305     TMPMEMFREE(mis_marker);
306     TMPMEMFREE(counter);
307 gross 2551 Paso_SparseMatrix_free(schur);
308     Paso_SparseMatrix_free(schur_withFillIn);
309 jfenwick 1851 if (Paso_noError()) {
310 artak 2524 if (verbose && level>0 && !out->coarsest_level) {
311 gross 2551 printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
312 jfenwick 1851 }
313     return out;
314     } else {
315     Paso_Solver_AMG_free(out);
316     return NULL;
317     }
318     }
319    
320     /**************************************************************/
321    
322     /* apply AMG precondition b-> x
323    
324     in fact it solves
325    
326 artak 2381 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
327 jfenwick 1851 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
328    
329     in the form
330    
331     b->[b_F,b_C]
332     x_F=invA_FF*b_F
333     b_C=b_C-A_CF*x_F
334     x_C=AMG(b_C)
335     b_F=b_F-A_FC*x_C
336     x_F=invA_FF*b_F
337     x<-[x_F,x_C]
338    
339     should be called within a parallel region
340     barrier synconization should be performed to make sure that the input vector available
341    
342     */
343    
344     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
345 artak 2107 dim_t i;
346 artak 2507 double time0=0;
347 gross 2551 double *r=NULL, *x0=NULL;
348 artak 2509 bool_t verbose=0;
349 artak 2507 #ifdef MKL
350 gross 2551 Paso_SparseMatrix *temp=NULL;
351     #else
352     #ifdef UMFPACK
353     Paso_UMFPACK_Handler * ptr=NULL;
354     #endif
355 artak 2507 #endif
356 gross 2551 r=MEMALLOC(amg->n,double);
357     x0=MEMALLOC(amg->n,double);
358 artak 2507
359 artak 2524 if (amg->coarsest_level) {
360 artak 2507
361     time0=Paso_timer();
362     #ifdef MKL
363 gross 2551 temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
364 artak 2507 #pragma omp parallel for private(i) schedule(static)
365     for (i=0;i<amg->A->len;++i) {
366     temp->val[i]=amg->A->val[i];
367     }
368     Paso_MKL1(temp,x,b,0);
369     Paso_SparseMatrix_free(temp);
370     #else
371 gross 2551 #ifdef UMFPACK
372     ptr=(Paso_UMFPACK_Handler *)(amg->solver);
373     Paso_UMFPACK1(&ptr,amg->A,x,b,0);
374     amg->solver=(void*) ptr;
375     #else
376     Paso_Solver_solveJacobi(amg->GS,x,b);
377     #endif
378 artak 2507 #endif
379 artak 2475 time0=Paso_timer()-time0;
380 artak 2507 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n\n\n",time0);
381    
382 jfenwick 1851 } else {
383 artak 1902 /* presmoothing */
384 artak 2507 time0=Paso_timer();
385 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
386 artak 2507 time0=Paso_timer()-time0;
387     if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
388 artak 1931 /* end of presmoothing */
389 artak 1939
390 artak 2507
391     time0=Paso_timer();
392 artak 1890 #pragma omp parallel for private(i) schedule(static)
393     for (i=0;i<amg->n;++i) r[i]=b[i];
394    
395     /*r=b-Ax*/
396     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
397 artak 1954
398 jfenwick 1851 /* b->[b_F,b_C] */
399 artak 1954 #pragma omp parallel for private(i) schedule(static)
400     for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
401    
402     #pragma omp parallel for private(i) schedule(static)
403     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
404 artak 1890
405 jfenwick 1851 /* x_F=invA_FF*b_F */
406 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
407 artak 1890
408 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
409     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
410 artak 1890
411 artak 2507 time0=Paso_timer()-time0;
412     if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
413    
414 jfenwick 1851 /* x_C=AMG(b_C) */
415     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
416 artak 1890
417 artak 2507 time0=Paso_timer();
418 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
419     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
420     /* x_F=invA_FF*b_F */
421 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
422 jfenwick 1851 /* x<-[x_F,x_C] */
423 artak 2113
424 artak 1954 #pragma omp parallel for private(i) schedule(static)
425     for (i=0;i<amg->n;++i) {
426     if (amg->mask_C[i]>-1) {
427 artak 2107 x[i]=amg->x_C[amg->mask_C[i]];
428 artak 1954 } else {
429 artak 2107 x[i]=amg->x_F[amg->mask_F[i]];
430 artak 1954 }
431 jfenwick 1851 }
432 artak 1954
433 artak 2507 time0=Paso_timer()-time0;
434     if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
435    
436 artak 1931 /*postsmoothing*/
437 artak 2507 time0=Paso_timer();
438 artak 1954 #pragma omp parallel for private(i) schedule(static)
439     for (i=0;i<amg->n;++i) r[i]=b[i];
440 artak 2107
441 artak 2442 /*r=b-Ax */
442 artak 1954 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
443 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
444 artak 2107
445     #pragma omp parallel for private(i) schedule(static)
446     for (i=0;i<amg->n;++i) x[i]+=x0[i];
447    
448 artak 2507 time0=Paso_timer()-time0;
449     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
450 artak 2509
451 artak 1931 /*end of postsmoothing*/
452    
453 jfenwick 1851 }
454 artak 1890 MEMFREE(r);
455 artak 1954 MEMFREE(x0);
456 gross 2551 return;
457 jfenwick 1851 }

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